Continuous quantum measurement of a double dot

TL;DR

This paper investigates how continuous weak measurement of a double quantum dot can lead to the gradual purification of its quantum state, highlighting the role of stochastic detector output and the quantum Zeno effect.

Contribution

It introduces a nonlinear Langevin equation describing the stochastic evolution of the double-dot density matrix under continuous measurement, emphasizing the purification process.

Findings

Gradual purification of the quantum state observed

Quantum Zeno effect demonstrated in the measurement process

Proposed experiments to validate the theory

Abstract

We consider the continuous measurement of a double quantum dot by a weakly coupled detector (tunnel point contact nearby). While the conventional approach describes the gradual system decoherence due to the measurement, we study the situation when the detector output is explicitly recorded that leads to the opposite effect: gradual purification of the double-dot density matrix. Nonlinear Langevin equation is derived for the random evolution of the density matrix which is reflected and caused by the stochastic detector output. Gradual collapse, gradual purification, and quantum Zeno effect are naturally described by the equation. We also discuss the possible experiments to confirm the theory.